In this paper we develop a nonequilibrium (NEQ) cell model to describe the dynamic operation of reactive distillation (RD) tray columns. The features of our model are: (1) use of the Maxwell-Stefan equations for describing mass transfer between fluid phases, (2) chemical reactions are assumed to take place only in the liquid phase, (3) coupling between mass transfer and chemical reactions within the diffusion layer is accounted for, and (4) the use of multiple well-mixed cells in the liquid and Vapour flow directions accounts for staging in either fluid phase. When the chemical reactions are suppressed, our model describes the dynamic behaviour of conventional distillation columns. We demonstrate the utility of the dynamic NEQ cell model by means of three case studies: (1) metathesis of 2-propene in an RD column, (2) distillation of methanol-iso-propanol-water, and (3) synthesis of methyl tert-buryl ether (MTBE) in an RD column. For comparison purposes we have also carried out dynamic simulations using the equilibrium stage (EQ) model. These case studies help us to draw the following conclusions. The introduction of staging in the liquid and vapour phases not only influences the steady-state performance, by increasing reaction conversion and separation capability, but also has a significant influence on column dynamics. With multiple cells per stage the column dynamics becomes much more sensitive to perturbations. Furthermore, we show that even when the NEQ cell model and EQ stage model exhibit almost identical steady-state characteristics, the dynamic responses of an RD column could even be qualitatively different. When operating close to the distillation boundary for nonreactive, conventional, distillation, small disturbances in feed compositions can lead to completely different product compositions.